It's impossible to discuss the movie in any depth without getting overly political, because it is a highly politically charged movie where Brad Bird voices all sorts of political statements covertly, from the value and inherent dignity of motherhood, to criticism of a litigation centered culture, to social libertarianism.
I can't discuss that or my opinion of it, but I can point out several things.
The movie has three villains, each of which represents a deranged version of the libertarian ideas Bob represents. Each of them in some fashion misuses their individual rights in a selfish way that works to destroy those very rights.
1) Oliver Sansweet, the man who sues Bob for saving him from himself (and his pack of lawyers): "Mr. Sansweet didn't ask to be saved. Mr. Sansweet didn't want to be saved...You didn't save my life! You ruined my death, that's what you did!" - Oliver Sansweet is challenging the right of an individual to intervene in anothers life. Oliver Sansweet defeats Bob. The world Sansweet creates with the help of his lawyers is one where no one can intervene in anyones life save through faceless bureaucracies, communication by lawyers, and impersonal bureaucratic jargon. He creates a world filled with fear, where no one is willing to risk standing out because even if they try to help, they'll be punished. And since no one can stand out, it's a world without heroes. Society tries to console itself for its loss by saying that the world is now filled with everyday heroes, but without rights the individual proves to have no power, as we see from the next villain...
2) Bob's boss at the insurance agency: Bob is trying to save the world one policy at a time. He tries to help, but he faces the same obstacles to being an ordinary hero as he faced being an extraordinary one. He's forced to act covertly. He lives in fear of lawyers and the corporation he works for. "We're supposed to help our people! Starting with our
stockholders. Bob a company is like an enormous clock." Bob's boss believes no matter what the team comes first. The individual should be a 'cooperative cog', and that a person's real job is to help the team succeed and only the team succeed. When Mr. Huph is informed that someone needs help, his only concern is whether or not they would be legally required to help: "Well, let's hope we don't cover him." He's not interested in duty or compassion. He's interested in the team (and hense himself) getting ahead. Mr. Huph defeats Bob. Bob's exceptional ability is of no value compared with Mr. Huph's authority and position in the world of lawyers, restrictions, and companies. When Bob loses it, Mr. Huph ultimately wins.
3) Syndrome: Contrary to what you might think, Syndrome is a super like Bob. Syndrome (like Edna) is a 'gadgeteer' - a super with the incredible ability to make things. Syndrome doesn't however want to help other people. Syndrome wants to be liked and admired. Where as Bob does what he feels he must whether he gets rewarded, thanked or not, Syndrome only really cares about the rewards - fame, respect, power, wealth. This isn't real heroism though. It's just the mask of heroism. Bob is a hero who wears a mask (whether an actual mask or the mask of being ordinary) to disguise his heroism, Syndrome is a self-centered individual that wears the mask of a hero. Syndrome's threat, "And when everyone's super...no one will be.", isn't really credible. Syndrome isn't actually going to share. If he wanted to share, he would have done so. He might be lying to himself or to Bob, but Syndrome simply isn't the sort that is trying to help or enable others. Syndrome is much more honest when Bob gets him monologuing, "Now you respect me, because I'm a threat. That's the way it works." Personal power as far as Syndrome is concerned isn't to help others, but to push down, intimidate, and subjegate others.
"Everyone's special, Dash....Which is another way of saying no one is."
After Oliver Sansweet, the world becomes afraid of anyone standing out as special. Everyone is required to be ordinary. People are punished for winning (being heroic) and rewarded for losing (failing to help others). No one wants an inspiration. Oddly, the world didn't become afraid of heroes because of someone like Syndrome. They didn't become afraid of people using their power to oppress them, they became afraid of people actually helping them. Consequently they live in a world were everyone is oppressed reutinely. What they didn't count on is that although they could take away everyone's freedom to be heroic, they couldn't prevent people from using their talents to oppress them precisely because those people didn't care about their rules. Only the people who actually cared to help were punished.
Bob tries to be a heroic insurance agent, but fails. Helen is heroicly being a mother, but even she is failing at the task because she's forced to push down and suppress her children to get them to confom. But as a result her children are unprepared to deal with real life or to stand on their own, which means she's failed at her most basic job - getting her children ready to live their lives without a parent. Her children can only survive in a world of mediocrity. When something real happens, they don't know what to do despite the fact that they are extraordinarily capable individuals.
The message of the movie is that we can't escape our need for heroes and that we can't let envy and greed rule the society. Everyone has a role. Everyone isn't born 'incredible', but its worth noting that you don't have to be incredible to be a hero. Nobody in the movie could have done what Bob did, but anybody could have been the hero Bob was trying to be at work or the mother Helen was trying to be at home. They just weren't, in part because they didn't have any heroes to inspire them to do so. Everyone had to help and support everyone else, and it was ok to celebrate extraordinary accomplishment if it was done in the service of everyone.